Question: Consider a cellular system in which each cell has only one channel (single server) and an infinite buffer for storage the calls. In this cellular

Consider a cellular system in which each cell has only one channel (single server) and an infinite buffer for storage the calls. In this cellular system, call arrival rates are discouraged, that is, the call rate is only λ/(n + 1) when there are n calls in the system. The interarrival times of calls are exponentially distributed. The call holding times are exponentially distributed with mean rate μ.

Develop expressions for the following:

(a) Steady-state probability P_n of n calls in the system.
(b) Steady-state probability P₀ of no calls in the system.
(c) Average number of calls in the system, L_S.
(d) Average dwell time, W_S.
(e) Average queue length, L_Q.

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